ε-Constrained Multiobjective Differential Evolution Using Linear Population Size Expansion

Constrained multiobjective optimization problems commonly arise in real-world applications. In the presence of constraints and multiple conflicting objectives, finding a set of feasible solutions which can best tradeoff different objectives is quite challenging. In this study, an ε-constrained multiobjective differential evolution using linear population size expansion is proposed to solve such a kind of problems. First, the ε-constraint-handling method, which originally solves constrained optimization problems with only one objective, is further improved to handle constraints in a multiobjective optimization way. Second, to achieve a better approximation to the feasible Pareto front, a linear population size expansion strategy is developed. Once enough feasible solutions have been found, the population size will be linearly increased to find more promising solutions. As a result, a simple yet efficient constrained multiobjective differential evolution is proposed. Experiments are conducted to evaluate the performance of the proposed algorithm on 35 benchmark test functions with different numbers of constraints and objectives. Obtained results are compared with seven state-of-the-art algorithms. Empirical results and comparisons demonstrate that our proposed algorithm achieves better or at least comparable performance to the competitors, and is capable of obtaining a set of representative feasible solutions for the selected real-world constrained multiobjective optimization problems, especially for highly constrained problems.